Gaming Hint Problem

发表于2016-02-18||
阅读次数：

Hao is playing a video game.

On the one hand, suppose there exists an hint for each movement. The probability that the hint is “to shot” is $p_1$. When the hint is “to shot” and the actual best movement is “to shot” with a probability of $p_2$. That if the hint does not imply him to shot but the real best movement is “to shot” has a probability of $p_3$.

On the other hand, the probability that Hao sees the hint is $p_4$. If he sees the hint then he will always shot, and if not then he will not shot. If he misses the hint then Hao will flip a fair coin to decide whether or not to shot.